BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:About small jumps of Lévy processes: approximation
s and estimation - Ester Mariucci (Université de V
ersailles Saint-Quentin-en-Yvelines)
DTSTART;TZID=Europe/London:20240424T094500
DTEND;TZID=Europe/London:20240424T103000
UID:TALK214156AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/214156
DESCRIPTION:Abstract: We consider the problem of estimating th
e density of the process associated with the small
jumps of a pure jump Lé\;vy process\, possi
bly of infinite variation\, from discrete observat
ions of one trajectory. The interest of such a que
stion lies on the observation that even when the L
é\;vy measure is known\, the density of the
increments of the small jumps of the process canno
t be computed. We discuss results both from low an
d high frequency observations. In a low frequency
setting\, assuming the Lé\;vy density associ
ated with the jumps larger than $\\eps\\in (0\,1]$
in absolute value is known\, \;a spectral&nbs
p\; estimator relying on the convolution structure
of the problem achieves \; minimax parametric
rates of convergence with respect to the integrat
ed $L_2$ loss\, up to a logarithmic factor. In a h
igh frequency setting\, we remove the assumption o
n the knowledge of the Lé\;vy measure of the
large jumps and show that the rate of convergence
depends both on the sampling scheme and on the be
haviour of the Lé\;vy measure in a neighborh
ood of zero. We show that the rate we find is mini
max up to a log-factor. \; An adaptive penaliz
ed procedure is studied to select the cutoff param
eter. These results are extended to encompass the
case where a Brownian component is present in the
Lé\;vy process. Furthermore\, we illustrate
the performances of our procedures through an exte
nsive simulation study.\nThis is a joint work with
Taher Jalal and Cé\;line Duval.
LOCATION:External
CONTACT:
END:VEVENT
END:VCALENDAR